13/12: Difference between revisions
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In [[13-limit]] [[just intonation]], '''13/12''' is the '''(lesser) tridecimal neutral second''' of about 138.6¢. It is a [[superparticular]] interval, as it is found in the harmonic series between the 13th and the 12th harmonics (between [[13/8]] and [[3/2]] in the octave). It is flat of the [[11-limit]] lesser neutral second of [[12/11]] by [[144/143]] (about 12.1¢), and sharp of the 13-limit large semitone of [[14/13]] by [[169/168]] (about 10.3¢). | In [[13-limit]] [[just intonation]], '''13/12''' is the '''(lesser) tridecimal neutral second''' of about 138.6¢. It is a [[superparticular]] interval, as it is found in the harmonic series between the 13th and the 12th harmonics (between [[13/8]] and [[3/2]] in the octave). It is flat of the [[11-limit]] lesser neutral second of [[12/11]] by [[144/143]] (about 12.1¢), and sharp of the 13-limit large semitone of [[14/13]] by [[169/168]] (about 10.3¢). | ||
== Approximation == | == Approximation == | ||
It is approximated to within about 0.11 [[cents]] by the 3-step interval of [[26edo]]. | It is approximated to within about 0.11 [[cents]] by the 3-step interval of [[26edo]]. | ||
{{Interval edo approximation|{{PAGENAME}}}} | {{Interval edo approximation|{{PAGENAME}}}} | ||
== Temperaments == | |||
13/12 can be used to generate [[bleu]] temperament in the 2.3.7.11.13 subgroup, mapping [[3/2]] to +5 generators, [[7/4]] to +7 generators, [[11/8]] to +4 generators, and [[13/8]] to +6 generators. | |||
A slightly sharp 13/12 generates [[glacier]] temperament, which equates 5 13/12's to 3/2 like bleu. This temperament has an extension to the 2.3.7.11.13.23.29 subgroup which is more complex but much more accurate than bleu. | |||
== See also == | == See also == | ||
* [[24/13]] – its [[octave complement]] | * [[24/13]] – its [[octave complement]] | ||